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This article deals with learning dictionaries for sparse approximation whose atoms are both adapted to a training set of signals and mutually incoherent. To meet this objective, we employ a dictionary learning scheme consisting of sparse approximation followed by dictionary update and we add to the latter a decorrelation step in order to reach a target mutual coherence level. This step is accomplished by an iterative projection method complemented by a rotation of the dictionary. Experiments on musical audio data and a comparison with the method of optimal coherence-constrained directions (mocod) and the incoherent k-svd (ink-svd) illustrate that the proposed algorithm can learn dictionaries that exhibit a low mutual coherence while providing a sparse approximation with better signal-to-noise ratio (snr) than the benchmark techniques.